{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 1\n",
    "\n",
    "Polynomial and Lagrange Interpolation\n",
    "\n",
    "26/02/2020\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXERCICE 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([0,1,2])\n",
    "y = np.array([0,4,0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a1 = -4\n",
      "a2 = 8\n",
      "a3 = 0\n"
     ]
    }
   ],
   "source": [
    "a1 = -4\n",
    "a2 = 8\n",
    "a3 = 0\n",
    "print('a1 = %i' %a1)\n",
    "print('a2 = %i' %a2)\n",
    "print('a3 = %i' %a3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(-1, 3, num=1000)\n",
    "ys = a1*xs**2 + a2*xs + a3\n",
    "plt.scatter(x, y, s=50, color='red')\n",
    "plt.plot( xs, ys, color='black');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([0,1,2])\n",
    "y = np.array([2,1,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a1 = 0\n",
      "a2 = -1\n",
      "a3 = 2\n"
     ]
    }
   ],
   "source": [
    "a1 = 0\n",
    "a2 = -1\n",
    "a3 = 2\n",
    "print('a1 = %i' %a1)\n",
    "print('a2 = %i' %a2)\n",
    "print('a3 = %i' %a3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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c3znnj4mJKaBoEm6ioqK49957SUtL+98x+1dffTWffPKJ19FECrUCKXzn3AHn3MHg8mKghJmdUxBzS+FVtWpVlixZwowZMwgEAiQkJDBixAh+++03r6OJFEoFUvhmVsnMLLhcNzjvDwUxtxRuZkbXrl3Ztm0bbdu2ZfDgwdStW5dNmzZ5HU2k0AnVYZmvAR8Dl5vZN2bWw8zuMbN7gkM6Amlmlgq8CNzsdAiGnILzzjuPOXPmMG/ePHbv3k3dunUZNGgQv/zyi9fRRAoNC9fe9fv9Ljk52esYEob27dvHAw88wLRp07jsssuYOnUqjRo18jqWSFgws43OOX926/RJWyl0KlSowNSpU1m2bBlHjhyhcePG9O7dm4yMDK+jiYQ1Fb4UWs2bN2fr1q307duXCRMmEB8fz7vvvut1LJGwpcKXQq1s2bK88MILrFmzhujoaFq1akW3bt344QcdEyByPBW+FAkNGjRg8+bNPPLII8yaNQufz8ecOXN0egaRLFT4UmSUKlWKYcOGkZycTJUqVejcuTMdOnRg165dXkcTCQsqfClyEhISWLduHaNGjeLdd98lNjaWadOmaW9fIp4KX4qk4sWL8+CDD5KamkpCQgI9evSgRYsWfPHFF15HE/GMCl+KtMsuu4wVK1YwceJEkpKSiI+PZ8yYMfz+++9eRxMpcCp8KfKioqK45557SE9P55prrqFfv340atSIQCDgdTSRAqXCl4hRpUoV3nnnHf7973+zfft2atWqxbBhwzhy5IjX0UQKhApfIoqZceuttxIIBOjQoQOPPfYYderUQafxkEigwpeIdO655/Laa6+xYMECvv/+e+rVq8dDDz2kk7FJkabCl4jWtm1b0tPT6dGjB8888ww1a9bko48+8jqWSL5Q4UvEO+uss5g8eTLLly/n2LFjNGnShF69enHgwAGvo4mElApfJKhp06Zs2bKFf/7zn0yePJm4uDjeeecdr2OJhIwKXySL6OhonnvuOdauXUv58uW54YYbuO222/j+++8zB2RkwJQpMGBA5ledklkKkVBd8WqamX1nZmk5rDcze9HMdpjZFjOrHYp5RfJLvXr12LRpE48//jhvvPEGsbGxvP7EE7gLLoB+/WDUqMyvlSvD6tVexxXJlVDt4U8HWp5gfSugevDWE5gYonlF8k2pUqV44okn2LhxIxdfdBFdhgyh/cGD7Dx0KHPAoUOZe/itW8PBg96GFcmFkBS+c24l8OMJhrQDZrpM64CzzOz8UMwtkt9q1KjBx3ffzbMlS7IM8AEvAf87FduxYzB7tmf5RHKroF7Drwx8neX+N8HH/g8z62lmyWaWvHfv3gKKJnJyxT77jP5HjrAFqE3mf1ObAZ9B5p7+jh1exhPJlbB609Y5N9k553fO+WNiYryOI/L/Va8O0dFcCiwH/gVsBGoAo0uW5PdLLvE0nkhuFFTh7wSqZLl/YfAxkcLhppsgKvPHJYrMPfx0Mvfy+x85QsPJk0lLy/aYBZGwUVCFvxDoGjxapz6w3zmnyxBJ4VGuHCxenPk1OhqAC6OjWVi2LK89/jiff/kltWvXZsiQIToZm4QtC8VVgMzsNaAJcA6wB3gcKAHgnJtkZgaMI/NInp+B251zJzxbld/vdzqhlYSdgwcz36DdsQMuvTRzz79sWb7//nv69u3LrFmziI+PZ+rUqdStW9frtBKBzGyjc86f7bpwveybCl8Ko7fffpt77rmHXbt2cf/99zN06FDKlCnjdSyJICcq/LB601aksLvhhhtIT0/nrrvu4rnnnqNGjRqsWLHC61gigApfJOTOPPNMJk2axIoVKzAzmjZtSs+ePdm/f7/X0STCqfBF8kmTJk3YsmULDz74IFOnTsXn87Fo0SKvY0kEU+GL5KMyZcowatQokpKSqFixIm3btqVLly7og4XiBRW+SAHw+/0kJyczdOhQ5s2bR2xsLLNmzSJcD5qQokmFL1JASpYsyaOPPsrmzZu59NJLufXWW2nTpg1ff/31yf+wSAio8EUKWFxcHGvWrOH5559nxYoVxMXFMWnSJI4dO+Z1NCniVPgiHihWrBj9+vVj69at1K1bl169etG0aVO2b9/udTQpwlT4Ih665JJLWLZsGVOnTiUlJYWaNWvyzDPPcPToUa+jSRGkwhfxmJlxxx13EAgEuO6663jooYdo0KABW7Zs8TqaFDEqfJEwccEFFzB//nzeeOMNvvrqK6688koee+wxfv31V6+jSRGhwhcJI2ZGp06dCAQCdOnShWHDhlG7dm3WrVvndTQpAlT4ImGoYsWKzJw5k8WLF5ORkUHDhg25//77OfTH9XRFToMKXySMtWrVirS0NHr16sULL7xAfHw877//vtexpJBS4YuEufLlyzN+/HhWrlxJiRIluPbaa+nRowc//fST19GkkFHhixQSjRs3JjU1lYEDBzJjxgx8Ph9vvfWW17GkEAlJ4ZtZSzP71Mx2mNnAbNZ3N7O9ZpYSvN0ZinlFIs0ZZ5zBU089RVJSEueeey5/+9vf6Ny5M3v27PE6mhQCeS58MysGjAdaAT6gi5n5shk62zmXGLxNyeu8IpHsyiuvZMOGDTz55JMsWLAAn8/HK6+8opOxyQmFYg+/LrDDOfe5c+4I8DrQLgTPKyInUKJECR5++GFSUlK44oor6Nq1K61bt+arr77yOpqEqVAUfmUg6+n+vgk+drwbzWyLmc01syrZPZGZ9TSzZDNL1vnCRXInNjaWVatW8eKLL7Jq1Sri4uIYP368TsYmf1JQb9ouAqo552oCy4AZ2Q1yzk12zvmdc/6YmJgCiiZS+EVFRXHfffeRlpZGgwYN6N27N9dccw2ffvqp19EkjISi8HcCWffYLww+9j/OuR+cc398PnwKcGUI5hWR41SrVo2lS5fy8ssvk5aWRkJCAiNHjtTJ2AQITeFvAKqb2cVmVhK4GViYdYCZnZ/lbltgWwjmFZFsmBndu3dn27ZtXH/99QwaNIh69eqRkpLidTTxWJ4L3zl3FOgNLCWzyN9wzqWb2VAzaxsc1sfM0s0sFegDdM/rvCJyYpUqVWLevHnMnTuXnTt34vf7GTx4MIcPH/Y6mnjEwvUwLr/f75KTk72OIVIk/Pjjj/Tv35/p06dz+eWXM3XqVK666iqvY0k+MLONzjl/duv0SVuRCHD22Wfz8ssvs3TpUg4fPkzjxo3p06cPBw8e9DqaFCAVvkgEadGiBWlpafTu3Ztx48YRHx/Pe++953UsKSAqfJEIU7Zs2f8ds1+6dGmuu+46br/9dn788Uevo0k+U+GLRKirrrqKlJQUHn74YV555RV8Ph/z5s3zOpbkIxW+SAQrXbo0Tz75JMnJyVxwwQV07NiRjh07snv3bq+jST5Q4YsIiYmJJCUlMXLkSN5++21iY2OZPn26TsZWxKjwRQTIPBnbgAEDSE1NJT4+nttvv53rrruOL7/80utoEiIqfBH5Py6//HI++ugjxo8fz8cff0x8fDxjx47VydiKABW+iPxJVFQU//jHP0hLS/vfMfuNGzdm2zadFaUwU+GLSI6qVq3K4sWLmTlzJp988gmJiYmMGDGC3377zetochpU+CJyQmbG3//+dwKBAO3bt2fw4MHUqVOHTZs2eR1NTpEKX0Ry5bzzzmP27NnMnz+fPXv2ULduXQYOHMgvv/zidTTJJRW+iJyS9u3bEwgE6N69O08//TSJiYmsWrXK61iSCyp8ETllFSpUYMqUKSxbtowjR45w9dVXc++995KRkeF1NDkBFb6InLbmzZuTlpZGv379mDhxInFxcSxZsuT/D8jIgClTYMCAzK/6heCpkBS+mbU0s0/NbIeZDcxmfSkzmx1cn2Rm1UIxr4h4Lzo6mueff541a9ZQtmxZWrduTdeuXfnhnXegcmXo1w9Gjcr8WrkyrF7tdeSIlefCN7NiwHigFeADupiZ77hhPYB9zrlLgeeBp/M6r4iElwYNGrB582YeffRRXnvtNWLbtOGNjAzcoUOZAw4dytzDb90adB5+T4RiD78usMM597lz7gjwOtDuuDHtgBnB5blAMzOzEMwtImGkVKlSDB06lI2DB3ORGTcBHYBvsw46dgxmz/YmYIQLReFXBr7Ocv+b4GPZjgleA3c/UPH4JzKznmaWbGbJe/fuDUE0EfFCzV9+Yd2xY4wC3iXzv/5TAQeZe/o7dngZL2KF1Zu2zrnJzjm/c84fExPjdRwROV3Vq1M8OpoHgS1AAnAncC3w+RlnwKWXehovUoWi8HcCVbLcvzD4WLZjzKw4cCbwQwjmFpFwdNNNEJVZL9WBFcBEYD1Q45dfeOH77/n99989DBiZQlH4G4DqZnaxmZUEbgYWHjdmIdAtuNwR+MDpRNsiRVe5crB4cebX6GiigHuio0mPjuavDRpw/8CBNGrUiEAg4HXSiJLnwg++Jt8bWApsA95wzqWb2VAzaxscNhWoaGY7gH8Cfzp0U0SKmEaN4NtvYcwYGDgQxoyhyu7dLFqzhldffZXt27eTmJjIsGHDOHLkiNdpI4KF64623+93ycnJXscQkXyyd+9e+vTpw+uvv06NGjWYOnUqderU8TpWoWdmG51z/uzWhdWbtiISOWJiYnjttddYsGABP/zwA/Xr1+ehhx7i559/9jpakaXCFxFPtW3blkAgQI8ePXjmmWdISEjgo48+8jpWkaTCFxHPnXnmmUyePJnly5dz7NgxmjRpQq9evThw4IDX0YoUFb6IhI2mTZuydetW+vfvz+TJk4mLi+Odd97xOlaRocIXkbBSpkwZnn32WT7++GPOOussbrjhBm699Vb06fu8U+GLSFiqW7cuGzdu5IknnmDOnDn4fD5ef/11wvXIwsJAhS8iYatkyZI8/vjjbNq0iUsuuYQuXbrQrl07du48/sP8khsqfBEJe/Hx8axdu5bnnnuO999/H5/Px0svvaS9/VOkwheRQqFYsWL885//ZOvWrVx55ZX07NmTZs2a8dlnn3kdrdBQ4YtIofKXv/yF5cuX89JLL7Fx40Zq1KjBc889p5Ox5YIKX0QKHTPjzjvvJBAI0Lx5cx544AEaNGhAWlqa19HCmgpfRAqtypUrs2DBAl5//XW+/PJLateuzRNPPKGTseVAhS8ihZqZcdNNNxEIBOjcuTNDhgyhdu3arF+/3utoYUeFLyJFwjnnnMO///1v3n77bfbv30+DBg3o37+/TsaWhQpfRIqU66+/nvT0dHr27Mno0aOpUaMGH3zwgdexwoIKX0SKnPLlyzNx4kQ+/PBDoqKiaNasGXfddRc//fST19E8lafCN7OzzWyZmW0Pfq2Qw7jfzSwleDv+8ociIvnimmuuYcuWLTz00ENMmzaNuLg4Fi6M3ArK6x7+QGC5c646sJycL134i3MuMXhrm8MYEZGQO+OMM3j66adJSkqiYsWKtGvXjptvvpnvvvvO62gFLq+F3w6YEVyeAbTP4/OJiOQLv99PcnIyw4YNY/78+fh8Pl599dWIOj1DXgv/POfcruDybuC8HMaVNrNkM1tnZjn+UjCznsFxyToVqoiEWsmSJXnkkUfYvHkz1atX57bbbqNNmzZ8/fXXXkcrECctfDN738zSsrm1yzrOZf6azOlXZdXgRXVvAV4ws79kN8g5N9k553fO+WNiYk71exERyRWfz8fq1at54YUXWLFiBXFxcUyaNIljx455HS1fnbTwnXPNnXPx2dwWAHvM7HyA4NdsXxRzzu0Mfv0c+BCoFbLvQETkNBQrVoy+ffuSlpZGvXr16NWrF3/961/Zvn2719HyTV5f0lkIdAsudwMWHD/AzCqYWang8jnAVUAgj/OKiITExRdfzHvvvcfUqVNJTU2lZs2ajBo1iqNHj3odLeTyWvgjgWvNbDvQPHgfM/Ob2ZTgmFgg2cxSgRXASOecCl9EwoaZcccddxAIBGjZsiUDBgygfv36pKameh0tpCxc36H2+/0uOTnZ6xgiEmGcc8ydO5fevXvz448/MnDgQB555BFKlSrldbRcMbONwfdM/0SftBURycLM6NSpE4FAgFtuuYXhw4dTq1YtPv74Y6+j5ZkKX0QkGxUrVmTGjBksWbKEQ4cOcdVVV9GvXz8OHjzodbTTpu/wW2gAAAfbSURBVMIXETmBli1bkpaWxj/+8Q/GjBlDjRo1WLZsmdexTosKX0TkJMqVK8e4ceNYuXIlJUuWpEWLFvTo0YN9+/Z5He2UqPBFRHKpcePGpKamMnDgQGbMmIHP52P+/Plex8o1Fb6IyCkoXbo0Tz31FOvXr6dSpUp06NCBzp07s2fPHq+jnZQKX0TkNPxxGcURI0awcOFCYmNjmTlzZlifjE2FLyJymkqUKMGgQYNISUkhNjaWbt260apVK/773/96HS1bKnwRkTy64oorWLVqFWPHjmX16tXEx8czfvz4sDsZmwpfRCQEoqKi6N27N2lpaTRs2JDevXtzzTXX8Omnn3od7X9U+CIiIVStWjXeffddpk+fTnp6OgkJCYwcOZLffvvN62gqfBGRUDMzunXrRiAQoE2bNgwaNIh69eqxefNmT3Op8EVE8kmlSpWYM2cO8+bN49tvv6VOnToMHjyYw4cPe5JHhS8iks86dOjAtm3b6Nq1KyNGjCAxMZE1a9YUeA4VvohIAahQoQLTpk1j6dKlHD58mMaNG3PfffeRkZFRYBlU+CIiBahFixakpaVx3333MX78eOLj41m6dGmBzJ2nwjezTmaWbmbHzCzbE+4Hx7U0s0/NbIeZDczLnCIihV3ZsmUZM2YMq1atokyZMrRs2ZLu3bvz448/5uu8ed3DTwM6ACtzGmBmxYDxQCvAB3QxM18e5xURKfSuuuoqNm/ezODBg3n11Vfx+XzMmzcv3+bLU+E757Y55072qYK6wA7n3OfOuSPA60C7vMwrIlJUlC5dmuHDh7NhwwYqV65Mx44d6dy5c758Srd4yJ/xzyoDX2e5/w1QL7uBZtYT6Alw0UUX5X8yEZEwkZiYSFJSEqNHj+bAgQNERYX+LdaTFr6ZvQ9UymbVYOfcglCGcc5NBiZD5kXMQ/ncIiLhrnjx4jz00EP59/wnG+Cca57HOXYCVbLcvzD4mIiIFKCCOCxzA1DdzC42s5LAzcDCAphXRESyyOthmX8zs2+ABsA7ZrY0+PgFZrYYwDl3FOgNLAW2AW8459LzFltERE5Vnt60dc7NB/50QUfn3LdA6yz3FwOL8zKXiIjkjT5pKyISIVT4IiIRQoUvIhIhVPgiIhHCnAvPzzeZ2V4gL5d+Pwf4PkRxQkm5To1ynRrlOjVFMVdV51xMdivCtvDzysySnXM5nsHTK8p1apTr1CjXqYm0XHpJR0QkQqjwRUQiRFEu/MleB8iBcp0a5To1ynVqIipXkX0NX0RE/q+ivIcvIiJZqPBFRCJEkSn8cL2gupmdbWbLzGx78GuFHMb9bmYpwVu+nT76ZN+/mZUys9nB9UlmVi2/spxCpu5mtjfL9rkzvzMF551mZt+ZWVoO683MXgzm3mJmtcMkVxMz259lez1WQLmqmNkKMwsEfxb7ZjOmwLdZLnMV+DYzs9Jmtt7MUoO5hmQzJrQ/j865InEDYoHLgQ8Bfw5jigGfAZcAJYFUwJfPuUYBA4PLA4Gncxh3sAC20Um/f+AfwKTg8s3A7DDI1B0Y58G/qauB2kBaDutbA0sAA+oDSWGSqwnwtgfb63ygdnC5HPCfbP4uC3yb5TJXgW+z4DYoG1wuASQB9Y8bE9KfxyKzh+/C94Lq7YAZweUZQPt8nu9EcvP9Z807F2hmZuZxJk8451YCP55gSDtgpsu0DjjLzM4Pg1yecM7tcs5tCi5nkHn9i8rHDSvwbZbLXAUuuA0OBu+WCN6OP4ompD+PRabwcym7C6rn91/8ec65XcHl3cB5OYwrbWbJZrbOzPLrl0Juvv//jXGZF6/ZD1TMpzy5zQRwY/AlgLlmViWb9V7w4t9TbjUIvlSwxMziCnry4EsPtcjca83K0212glzgwTYzs2JmlgJ8ByxzzuW4vULx85inC6AUtIK8oPqpOFGurHecc87McjoOtqpzbqeZXQJ8YGZbnXOfhTprIbUIeM0596uZ3U3mHk9TjzOFs01k/ns6aGatgbeA6gU1uZmVBeYB/ZxzBwpq3pM5SS5Ptplz7ncg0czOAuabWbxzLtv3ZkKhUBW+C9MLqp8ol5ntMbPznXO7gv91/S6H59gZ/Pq5mX1I5l5IqAs/N9//H2O+MbPiwJnADyHOcUqZnHNZ559C5vsi4SBf/j3lVdYyc84tNrMJZnaOcy7fTxJmZiXILNVXnXNvZjPEk212slxebrPgnD+Z2QqgJZC18EP68xhpL+l4cUH1hUC34HI34E//EzGzCmZWKrh8DnAVEMiHLLn5/rPm7Qh84ILvGOWTk2Y67jXetmS+BhsOFgJdg0ee1Af2Z3n5zjNmVumP13nNrC6ZP+f5+Uv7j3kNmApsc86NzmFYgW+z3OTyYpuZWUxwzx4zOwO4FvjkuGGh/XksyHel8/MG/I3M1wN/BfYAS4OPXwAszjKuNZnv0n9G5ktB+Z2rIrAc2A68D5wdfNwPTAkuNwS2knmEylagRz7m+dP3DwwF2gaXSwNzgB3AeuCSAthGJ8v0FJAe3D4rgCsK6N/Ua8Au4Lfgv60ewD3APcH1BowP5t5KDkeHeZCrd5bttQ5oWEC5GpH5puMWICV4a+31NstlrgLfZkBNYHMwVxrwWPDxfPt51KkVREQiRKS9pCMiErFU+CIiEUKFLyISIVT4IiIRQoUvIhIhVPgiIhFChS8iEiH+H5zwciIXMREqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(-1, 3, num=1000)\n",
    "ys = a1*xs**2 + a2*xs + a3\n",
    "plt.scatter(x, y, s=50, color='red')\n",
    "plt.plot( xs, ys, color='black');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1bis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([0,10,20,30])\n",
    "y = np.array([-250,0,50,-100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a1 = -1\n",
      "a2 = 35\n",
      "a3 = -250\n"
     ]
    }
   ],
   "source": [
    "a1 = -1\n",
    "a2 = 35\n",
    "a3 = -250\n",
    "print('a1 = %i' %a1)\n",
    "print('a2 = %i' %a2)\n",
    "print('a3 = %i' %a3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(-1, 40, num=1000)\n",
    "ys = a1*xs**2 + a2*xs + a3\n",
    "plt.scatter(x, y, s=50, color='red')\n",
    "plt.plot( xs, ys, color='black');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXERCICE 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Lagrange_interpolation():\n",
    "    \"\"\"x, y : data points in numpy.array type \"\"\"\n",
    "    def __init__(self, x=x, y=y):\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "    \n",
    "    \n",
    "    def Lagrange_coefficients (self, e): \n",
    "        total = 0\n",
    "        for j in range(len(self.x)):\n",
    "            yj = self.y[j]\n",
    "                \n",
    "            tot_mul = 1\n",
    "            for i in range(len(self.x)):\n",
    "                if i == j:\n",
    "                    continue\n",
    "                xi, xj = self.x[i], self.x[j]\n",
    "                tot_mul *= (e - xi) / float(xj - xi)\n",
    "       \n",
    "            total += yj * tot_mul\n",
    "                \n",
    "        return(total)\n",
    "    \n",
    "    def plot_point(self):\n",
    "        return (plt.scatter( x, y, s=50, color='red'))\n",
    "        \n",
    "    \n",
    "    def plot_polynomial(self):\n",
    "        xs = np.linspace(self.x[0]-1, self.x[len(self.x)-1]+1, num=1000)\n",
    "        l=[]\n",
    "        for i in xs :\n",
    "            l.append(self.Lagrange_coefficients (i))\n",
    "        self.plot_point()\n",
    "        return (plt.plot( xs, l, color='black'))\n",
    "        \n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([0,1,2])\n",
    "y = np.array([-1,-1,7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x936 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(13, 13))\n",
    "lag = Lagrange_interpolation(x,y)\n",
    "lag.plot_polynomial();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(-1, 3, num=1000)\n",
    "ys = -0.5*(xs-1)*(xs - 2) + xs*(xs-2) + 7/2*xs*(xs-1) \n",
    "plt.scatter(x, y, s=50, color='red')\n",
    "plt.plot( xs, ys, color='black');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2bis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([-1,0,1, 2])\n",
    "y = np.array([3,-4,5,-6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x936 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(13, 13))\n",
    "lag = Lagrange_interpolation(x,y)\n",
    "lag.plot_polynomial();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(-2, 3, num=1000)\n",
    "ys = -6*xs**3 + 8*xs**2 + 7*xs -4\n",
    "plt.scatter(x, y, s=50, color='red')\n",
    "plt.plot( xs, ys, color='black');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXERCICE 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([0,1,3, 4])\n",
    "y = np.array([1,0,2,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x936 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(13, 13))\n",
    "lag = Lagrange_interpolation(x,y)\n",
    "lag.plot_polynomial();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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